Advertisements
Advertisements
प्रश्न
Find the remainder when x4 – 3x2 + 2x + 1 is divided by x – 1.
Advertisements
उत्तर
By remainder theorem we know that when a polynomial f(x) is divided by x – a, then the remainder is f(a).
f(x) = x4 – 3x2 + 2x + 1
Remainder = f(1)
= (1)4 – 3(1)2 + 2(1) + 1
= 1 – 3 + 2 + 1
= 1
APPEARS IN
संबंधित प्रश्न
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
What number should be subtracted from x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?
use the rernainder theorem to find the factors of ( a-b )3 + (b-c )3 + ( c-a)3
The polynomial f(x) = ax4 + x3 + bx2 - 4x + c has (x + 1), (x-2) and (2x - 1) as its factors. Find the values of a,b,c, and remaining factor.
Find the remainder when the polynomial f(x) = 2x4 - 6x3 + 2x2 - x + 2 is divided by x + 2.
Using remainder theorem, find the value of a if the division of x3 + 5x2 – ax + 6 by (x – 1) leaves the remainder 2a.
Check whether p(x) is a multiple of g(x) or not:
p(x) = 2x3 – 11x2 – 4x + 5, g(x) = 2x + 1
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
For what value of m is x3 – 2mx2 + 16 divisible by x + 2?
Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]
